A Parallel Algorithm for the Two-Dimensional Cutting Stock Problem

  • Luis García
  • Coromoto León
  • Gara Miranda
  • Casiano Rodríguez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4128)


Cutting Stock Problems (CSP) arise in many production industries where large stock sheets must be cut into smaller pieces. We present a parallel algorithm – based on Viswanathan and Bagchi algorithm (VB) – solving the Two-Dimensional Cutting Stock Problem (2DCSP). The algorithm guarantees the processing of best nodes first and does not introduce any redundant combinations – others than the already present in the sequential version. The improvement is orthogonal to any other sequential improvements. Computational results of an OpenMP implementation confirm the optimality of the algorithm. We also produce a new syntactic based reformulation of the 2DCSP problem which leads to a concise representation of the solutions. A highly efficient data structure to store subproblems is introduced.


Parallel Algorithm Exact Algorithm Packing Problem Open List Algorithmic Skeleton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sweeney, P.E., Paternoster, E.R.: Cutting and Packing Problems: A categorized, application-orientated research bibliography. Journal of the Operational Research Society 43(7), 691–706 (1992)zbMATHGoogle Scholar
  2. 2.
    Dyckhoff, H.: A Typology of Cutting and Packing Problems. European Journal of Operational Research 44(2), 145–159 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dowsland, K.A., Dowsland, W.B.: Packing Problems. European Journal of Operational Research 56(1), 2–14 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Burke, E., Kendall, G.: Applying Simulated Annealing and the No Fit Polygon to the Nesting Problem. In: Arabnia, H.R.(ed.) Proceedings of the International Conference on Artificial Intelligence (IC-AI 1999). vol. 1, pp. 51–57. CSREA Press (1999),, Scholar
  5. 5.
    Maouche, S., Bounsaythip, C.: Optimizing Textile Shape Placement by Tree Genetic Annealing. In: Proceedings of the Society for Computer Simulation Conference (SCSC 1996) (1996), Salah.Maouche@univ-lille1.frGoogle Scholar
  6. 6.
    Roussel, G., Maouche, S.: Automatic Lay Planning for Irregular Shapes on Plain Fabric. Search in Direct Graph and ε-Admissible Resolution. In: Proceedings of the XVI IFIP-TC7 Conference, Compiégne, France (July 1993)Google Scholar
  7. 7.
    Christofides, N., Whitlock, C.: An Algorithm for Two-Dimensional Cutting Problems. Operations Research 25(1), 30–44 (1977)zbMATHCrossRefGoogle Scholar
  8. 8.
    Viswanathan, K.V., Bagchi, A.: Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems. Operations Research 41(4), 768–776 (1993)zbMATHCrossRefGoogle Scholar
  9. 9.
    Hifi, M.: An Improvement of Viswanathan and Bagchi’s Exact Algorithm for Constrained Two-Dimensional Cutting Stock. Computer Operations Research 24(8), 727–736 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Cung, V.D., Hifi, M., Le-Cun, B.: Constrained Two-Dimensional Cutting Stock Problems: A Best-First Branch-and-Bound Algorithm. Technical Report 97/020, Laboratoire PRiSM - CNRS URA 1525. Université de Versailles, Saint Quentin en Yvelines. 78035 Versailles Cedex, FRANCE (1997)Google Scholar
  11. 11.
    Tschöke, S., Holthöfer, N.: A New Parallel Approach to the Constrained Two-Dimensional Cutting Stock Problem. In: Ferreira, A., Rolim, J. (eds.) Parallel Algorithms for Irregularly Structured Problems, pp. 285–300. Springer, Berlin, Germany (1995), Google Scholar
  12. 12.
    Nicklas, L.D., Atkins, R.W., Setia, S.K., Wang, P.Y.: The Design and Implementation of a Parallel Solution to the Cutting Stock Problem. Concurrency - Practice and Experience 10(10), 783–805 (1998)CrossRefGoogle Scholar
  13. 13.
    Wang, P.Y.: Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems. Operations Research 31(3), 573–586 (1983)zbMATHCrossRefGoogle Scholar
  14. 14.
    Gilmore, P.C., Gomory, R.E.: The Theory and Computation of Knapsack Functions. Operations Research 14, 1045–1074 (1966)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Tschöke, S., Polzer, T.: Portable parallel branch-and-bound library - PPBB-lib (1996)Google Scholar
  16. 16.
    Alba, E.: et al: MaLLBa: A Library of Skeletons for Combinatorial Optimization. In: Monien, B., Feldmann, R.L. (eds.) Euro-Par 2002. LNCS, vol. 2400, pp. 927–932. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Le-Cun, B., Roucairol, C.: BOB: a unified platform for implementing branch-and-bound like algorithms (1995)Google Scholar
  18. 18.
    Group, D.O.R.: Library of Instances (Two-Constraint Bin Packing Problem),
  19. 19.
    Hopper, E., Turton, C.H.: An Empirical Investigation of Meta-heuristic and Heuristic Algorithms for a 2D Packing Problem xt (1999),

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Luis García
    • 1
  • Coromoto León
    • 1
  • Gara Miranda
    • 1
  • Casiano Rodríguez
    • 1
  1. 1.Dpto. Estadística, I. O. y ComputaciónUniversidad de La LagunaLa LagunaSpain

Personalised recommendations